Editorial 275 
We may adopt a similar process to find the standard-deviation of the second 
moment of an array in a sample. For an array of constant size rip we have 
Mean (8,,;..)= = i (l - i) |(l - i) - (l - i) ^..j , 
where ^/Xj and refer to the values in the sampled population. Thus 
Mean ( V,y= = (l - |) |f 1 - ^) - 3) + 2} , 
lip \ »p/ [\ tip 
and, summing for all values of p, 
Accordingly we require to find S j — S (^^^^ ii'ii'l ~ ^ • Writing 
t as before = — — ^ , we have 2- = C + 1- and after sonue reductions 
j 
Accordingly if ^/Xo be the second moment of the Vp array in a sample of N, 
.,(„ft-.,){(>-^,y-(:.l.l)(i-l)-(..ij)(I ^ 
1 \= 
- 10 
11 
•(N). 
It is usually given the value ~^jL ^ ^^yd further the assumption is made that {8a „ )- 
Hp 
may be neglected in 'io-^^Scr,,^^ + (Scr,,^,)- = Sjj/u.,, so that we obtain the value 
^ (0). 
(Tnp 
Now whatever may be said for this result the method by which it is reached is 
distinctly defective and this not merely because it assumes normality. We have 
in fact for any distribution of size il/ 
o- = V^tia- 
Now let us measure a from the mean value a of the sampled population and fj,.. 
